Place the eggs in a saucepan, cover them with 1 inch of water and bring the water to a full boil.
Cover the pan, remove it from the heat and let the eggs stand for 12 minutes so the yolks are fully set.
Transfer the eggs to ice water for 5 minutes, then peel and chop them into 1/3-inch pieces.
Fold the eggs with the mayonnaise, pickles, celery, Dijon, salt and black pepper without mashing the whites smooth.
Chill the egg salad for 20 minutes, then divide it over 4 bread slices and top each with a lettuce leaf.
Close with the remaining bread and cut each sandwich in half.